Transitivity of The delta^n-Relation in Hypergroups

Saeed Mirvakili, Peyman Ghiasvand


The $\delta^n$-relation was introduced by Leoreanu-Fotea et. al.\cite{130}. In this article, we introduce the concept of$\delta^{n}$-heart of a hypergroup and we determine necessary andsufficient conditions for the relation $\delta^{n}$ to betransitive. Moreover, we determine a family $P_{\sigma}(H)$ ofsubsets of a hypergroup $H$ and we give sufficient conditionssuch that the geometric space $(H, P_{\sigma}(H))$ is stronglytransitive and the relation $\delta^n$ is transitive.


Geometric spaces, Hypergroup, strongly regular relation

Full Text:



bibitem{199} S. M. Anvariyeh, B. Davvaz, {it Stronglg transitive geometric spaces associated to hypermodules}, Journal of Algebra,

(2009), 1340-1359.

bibitem{2} P. Corsini, {it Prolegomena of hypergroup theory }, Aviani Editore, 1993.

bibitem{3} P. Corsini and V. Leoreanu, {it Applications of hyperstructure theory},

Advances in Mathematics, Kluwer Academic Publishers, 2003.

bibitem{9} P. Corsini and V. Leoreanu, {it About the heart of a hypergroup}, Acta Univ. Carolin., 37 (1996) 17-28.

bibitem{80} B. Davvaz, V. Leoreanu-Fotea, {it Hyperring Theory and

Applications}, International Academic Press, USA, 2007.

bibitem{88} B. Davvaz, M. Karimian , {it On the $gamma^{*}$-complete hypergroups}, European J. Combin., 28 (2007) 86-93.

bibitem{10} D. Freni, {it A new characterization of the derived

hypergroup via strongly regular equivalences}, Comm. Algebra,

(8) (2002) 3977-3989.

bibitem{100} D. Freni, {it Strongly transitive geometric spaces: Applications to hypergroups and semigroups theory},

Comm. Algebra, 32(8) (2004) 969-988.

bibitem{101} D. Freni, {it Une note sur le coeur $d^{,}$un hypergroupe et

sur la cl^{o}ure $beta^{*}$ de $beta$ }, Riv. Mat. Pura Appl.,

(8) (1970) 307-312.

bibitem{190} M. Gutan, {it Properties of hyperproducts and the relation $beta$ in quasihpergroups},

Ratio Mathmatica, 12 (1997) 19-34.

bibitem{140} M. Koskas, {it Groupoides, demi-hypergroupes et hypergroupes},

J. Math. Pures Appl., 49 (1970) 155-192.

bibitem{120} M. Krasner, {it A class of hyperrings and hyperfields},

Intern. J. Math. Math. Sci., 6(2) (1983) 307-312.

bibitem{130} V. Leoreanu-Fotea, M. Jafarpour and S. Sh. Mousavi,

{it The relation $delta^{n}$ and multisemi-direct hyperproducts

of hypergroups}, Comm. Algebra, 40 (2012) 3597-3608.

bibitem{121} F. Marty, {it Sur une generalization de la notion de groupe}, $8^{iem}$ congres Math. Scandinaves,

Stockholm, (1934) 45-49.

bibitem{123} S. Mirvakili, S. M. Anvariyeh and B. Davvaz,

{it Transitivity of $Gamma$-relation on hyperfields}, Bull.

Math. Soc. Sci. Math. Roumanie, Tome 51(99) No. 3 (2008) 233-243.

bibitem{13} S. Mirvakili, S.M. Anvariyeh and B. Davvaz,

{it On $alpha$-relation and transitivity conditions of

$alpha$}, Comm. Algebra, 36 (2008) 1695–1703.

bibitem{299} S. Mirvakili and B. Davvaz, {it Strongly transitive geometric spaces: applications to hyperrings,}

Revista Uni'{o}n Matem'{a}tica Argentina, 53(1) (2012) 43-53.

bibitem{17} T. Vougiouklis, {it Hyperstructures and Their Representations},

Hadronice Press, Inc., Palm Harber, USA, (1994).

bibitem{16} T. Vougiouklis, {it The fundamental relation in hyperrings. The

general hyperfield}, Proc. Fourth Int. Congress on Algebraic

Hyperstructures and Applications (AHA 1990), World Scientific,

(1991) 203-211.



  • There are currently no refbacks.

Journal of the Indonesian Mathematical Society
Mathematics Department, Universitas Gadjah Mada
Senolowo, Sinduadi, Mlati, Sleman Regency, Special Region of Yogyakarta 55281, Telp. (0274) 552243

p-ISSN: 2086-8952 | e-ISSN: 2460-0245

Journal of the Indonesian Mathematical Society is licensed under a Creative Commons Attribution 4.0 International License

web statistics
View My Stats